Solutions to the fast Fourier transform (FFT) and finite impulse response (FIR) algorithms are required for signal processing in numerous engineering applications. Applications of both the FFT and FIR algorithms are abundantly described in the engineering literature.
The FFT is an algorithm for calculating the Discrete Fourier Transform (DFT) and its inverse.
An FIR filter is a type of a digital filter whose impulse response fades to zero after a sufficiently long time.
Increased efficiency in calculating FFT and FIR values is a constantly present goal for designers of signal processing systems.